Question: Emily is 4 times as old as William and is also 30 years older than William. How old is Emily?
Answer: We can use the given information to write down two equations that describe the ages of Emily and William. Let Emily's current age be $e$ and William's current age be $w$ $e = 4w$ $e = w + 30$ Now we have two independent equations, and we can solve for our two unknowns. One way to solve for $e$ is to solve the second equation for $w$ and substitute that value into the first equation. Solving our second equation for $w$ , we get: $w = e - 30$ . Substituting this into our first equation, we get the equation: $e = 4$ $(e - 30)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e = 4e - 120$ Solving for $e$ , we get: $3 e = 120$ $e = 40$.